Newform orbit 731.2.e.b

• Label: 731.2.e.b
• Level: $731$
• Weight: $2$
• Character orbit: 731.e
• Analytic conductor: $5.837$
• Analytic rank: $0$
• Dimension: $58$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.83706438776\)
Analytic rank:	\(0\)
Dimension:	\(58\)
Relative dimension:	\(29\) over \(\Q(\zeta_{3})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9}+O(q^{10}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
307.1	−2.61335			1.52887	−	2.64809i	4.82960			−0.766598	+	1.32779i	−3.99548	+	6.92038i	−0.834694	−	1.44573i	−7.39472			−3.17491	−	5.49911i	2.00339	−	3.46997i
307.2	−2.46945			−0.974328	+	1.68758i	4.09816			0.310056	−	0.537033i	2.40605	−	4.16740i	1.71828	+	2.97615i	−5.18130			−0.398628	−	0.690445i	−0.765666	+	1.32617i
307.3	−2.46652			0.742625	−	1.28626i	4.08373			0.428499	−	0.742181i	−1.83170	+	3.17260i	−2.43048	−	4.20972i	−5.13956			0.397017	+	0.687654i	−1.05690	+	1.83061i
307.4	−2.24624			−0.247428	+	0.428559i	3.04561			−0.237822	+	0.411920i	0.555785	−	0.962647i	−0.154590	−	0.267757i	−2.34870			1.37756	+	2.38600i	0.534206	−	0.925272i
307.5	−2.08718			−1.33964	+	2.32032i	2.35632			−2.10822	+	3.65155i	2.79606	−	4.84292i	0.688078	+	1.19179i	−0.743705			−2.08925	−	3.61869i	4.40024	−	7.62144i
307.6	−1.72289			−1.55986	+	2.70176i	0.968349			1.14718	−	1.98697i	2.68747	−	4.65483i	−2.28646	−	3.96026i	1.77742			−3.36633	−	5.83066i	−1.97646	+	3.42332i
307.7	−1.53983			0.868079	−	1.50356i	0.371078			0.736400	−	1.27548i	−1.33669	+	2.31522i	0.767588	+	1.32950i	2.50826			−0.00712137	−	0.0123346i	−1.13393	+	1.96403i
307.8	−1.48275			−0.591829	+	1.02508i	0.198553			0.830949	−	1.43925i	0.877535	−	1.51994i	−0.706420	−	1.22356i	2.67110			0.799477	+	1.38474i	−1.23209	+	2.13404i
307.9	−1.32448			1.04438	−	1.80892i	−0.245749			1.40548	−	2.43436i	−1.38326	+	2.39588i	0.178508	+	0.309184i	2.97445			−0.681454	−	1.18031i	−1.86153	+	3.22427i
307.10	−1.12544			1.19443	−	2.06882i	−0.733389			−2.16193	+	3.74458i	−1.34426	+	2.32833i	−1.34379	−	2.32751i	3.07626			−1.35334	−	2.34406i	2.43312	−	4.21429i
307.11	−1.09472			0.124885	−	0.216307i	−0.801596			−1.31747	+	2.28193i	−0.136714	+	0.236795i	0.589522	+	1.02108i	3.06695			1.46881	+	2.54405i	1.44226	−	2.49806i
307.12	−0.517241			−1.48646	+	2.57463i	−1.73246			0.969459	−	1.67915i	0.768860	−	1.33171i	1.00663	+	1.74354i	1.93058			−2.91915	−	5.05612i	−0.501444	+	0.868526i
307.13	−0.482661			−0.0594428	+	0.102958i	−1.76704			0.220118	−	0.381256i	0.0286908	−	0.0496939i	−2.49924	−	4.32882i	1.81820			1.49293	+	2.58584i	−0.106243	+	0.184018i
307.14	−0.267888			−0.791039	+	1.37012i	−1.92824			−1.21931	+	2.11190i	0.211910	−	0.367038i	2.34329	+	4.05870i	1.05233			0.248515	+	0.430440i	0.326638	−	0.565753i
307.15	0.0823862			0.281246	−	0.487132i	−1.99321			−0.854403	+	1.47987i	0.0231708	−	0.0401330i	−0.768980	−	1.33191i	−0.328986			1.34180	+	2.32407i	−0.0703910	+	0.121921i
307.16	0.175605			1.59696	−	2.76601i	−1.96916			1.26069	−	2.18359i	0.280434	−	0.485725i	−0.781954	−	1.35438i	−0.697005			−3.60054	−	6.23632i	0.221384	−	0.383449i
307.17	0.428243			−1.51618	+	2.62610i	−1.81661			−1.16373	+	2.01564i	−0.649294	+	1.12461i	−0.814374	−	1.41054i	−1.63444			−3.09761	−	5.36521i	−0.498360	+	0.863184i
307.18	0.504225			0.395848	−	0.685630i	−1.74576			1.62259	−	2.81041i	0.199597	−	0.345712i	1.77182	+	3.06888i	−1.88870			1.18661	+	2.05527i	0.818151	−	1.41708i
307.19	1.34037			−0.719541	+	1.24628i	−0.203418			2.16961	−	3.75787i	−0.964449	+	1.67047i	−1.07792	−	1.86701i	−2.95339			0.464522	+	0.804575i	2.90807	−	5.03692i
307.20	1.35318			1.03357	−	1.79019i	−0.168903			0.832416	−	1.44179i	1.39860	−	2.42245i	−1.69298	−	2.93233i	−2.93492			−0.636523	−	1.10249i	1.12641	−	1.95100i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
43.c	even	3	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	731.2.e.b	✓	58
43.c	even	3	1	inner	731.2.e.b	✓	58

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
731.2.e.b	✓	58	1.a	even	1	1	trivial
731.2.e.b	✓	58	43.c	even	3	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^29 - T2^28 - 42*T2^27 + 39*T2^26 + 783*T2^25 - 669*T2^24 - 8553*T2^23 + 6645*T2^22 + 60871*T2^21 - 42341*T2^20 - 296935*T2^19 + 181135*T2^18 + 1016856*T2^17 - 528872*T2^16 - 2460982*T2^15 + 1048989*T2^14 + 4175764*T2^13 - 1376685*T2^12 - 4847784*T2^11 + 1130073*T2^10 + 3673059*T2^9 - 521316*T2^8 - 1670608*T2^7 + 112107*T2^6 + 396312*T2^5 - 11956*T2^4 - 42015*T2^3 + 1227*T2^2 + 1350*T2 - 97